{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/83929"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/83929","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Non-Smooth Dynamics and Control of Tapping Mode Atomic Force Microscopy","abstract":"The case of co-dimension two grazing characterized by simultaneous tangential contact of a solution trajectory as well as a solution branch with the discontinuity surface is also presented. Analytical conditions are formulated to locate the co-dimension two grazing point and discontinuity-mapping technique is used to obtain a normal form description of the near-grazing dynamics. In addition to the non-smooth vector field, the relative strength of the vector fields on either side of the discontinuity surface is shown to be critical in determining the occurrence of discontinuity-induced isola and branch-point bifurcations. This result motivates a feedback strategy which modifies the near-grazing dynamics to ensure the persistence of the grazing solution trajectory beyond grazing. The feedback scheme applied to a linear impacting oscillator, and a dynamic model of tapping-mode atomic force microscope ensures persistence of the grazing solution trajectory by preventing loss of stability through a discontinuity induced saddle-node bifurcation.","abstract_html":"The case of co-dimension two grazing characterized by simultaneous tangential contact of a solution trajectory as well as a solution branch with the discontinuity surface is also presented. Analytical conditions are formulated to locate the co-dimension two grazing point and discontinuity-mapping technique is used to obtain a normal form description of the near-grazing dynamics. In addition to the non-smooth vector field, the relative strength of the vector fields on either side of the discontinuity surface is shown to be critical in determining the occurrence of discontinuity-induced isola and branch-point bifurcations. This result motivates a feedback strategy which modifies the near-grazing dynamics to ensure the persistence of the grazing solution trajectory beyond grazing. The feedback scheme applied to a linear impacting oscillator, and a dynamic model of tapping-mode atomic force microscope ensures persistence of the grazing solution trajectory by preventing loss of stability through a discontinuity induced saddle-node bifurcation.","abstract_has_math":false,"creators":["Misra, Sambit"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Dankowicz, Harry"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-25T21:12:45Z","date_published":"2015-09-25T21:12:45Z","updated_at":"2026-07-22T22:26:22Z","subjects":["Engineering, Mechanical"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3363041"],"render_values":[{"text":"(MiAaPQ)AAI3363041","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/83929","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dankowicz, Harry"]},{"key":"dc:creator","label":"Author","values":["Misra, Sambit"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T21:12:45Z","10000-01-01","2009"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering, Mechanical"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/83929","(MiAaPQ)AAI3363041"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The case of co-dimension two grazing characterized by simultaneous tangential contact of a solution trajectory as well as a solution branch with the discontinuity surface is also presented. Analytical conditions are formulated to locate the co-dimension two grazing point and discontinuity-mapping technique is used to obtain a normal form description of the near-grazing dynamics. In addition to the non-smooth vector field, the relative strength of the vector fields on either side of the discontinuity surface is shown to be critical in determining the occurrence of discontinuity-induced isola and branch-point bifurcations. This result motivates a feedback strategy which modifies the near-grazing dynamics to ensure the persistence of the grazing solution trajectory beyond grazing. The feedback scheme applied to a linear impacting oscillator, and a dynamic model of tapping-mode atomic force microscope ensures persistence of the grazing solution trajectory by preventing loss of stability through a discontinuity induced saddle-node bifurcation.","Made available in DSpace on 2015-09-25T21:12:45Z (GMT). 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Analytical conditions are formulated to locate the co-dimension two grazing point and discontinuity-mapping technique is used to obtain a normal form description of the near-grazing dynamics. In addition to the non-smooth vector field, the relative strength of the vector fields on either side of the discontinuity surface is shown to be critical in determining the occurrence of discontinuity-induced isola and branch-point bifurcations. This result motivates a feedback strategy which modifies the near-grazing dynamics to ensure the persistence of the grazing solution trajectory beyond grazing. The feedback scheme applied to a linear impacting oscillator, and a dynamic model of tapping-mode atomic force microscope ensures persistence of the grazing solution trajectory by preventing loss of stability through a discontinuity induced saddle-node bifurcation.","Made available in DSpace on 2015-09-25T21:12:45Z (GMT). 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